Sheet-like structure, shape estimation method, and spacecraft

ABSTRACT

[Object] To provide a sheet-like structure capable of highly accurately estimating a sheet-like shape. 
     [Solving Means] A sheet-like structure includes a sheet-like member and a plurality of detection sensors. The sheet-like member extends along an in-plane direction orthogonal to a thickness direction and receives light incident on the sheet-like member. The plurality of detection sensors are dispersedly arranged on the sheet-like member along the in-plane direction and are for detecting an incident angle of the light with respect to the sheet-like member at each arrangement position of the plurality of detection sensors.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.16/627,095, filed Dec. 27, 2019; which is the U.S. national stageapplication of International Patent Application No. PCT/JP2018/013902,filed Mar. 30, 2018, which claims the benefit under 35 U.S.C. § 119 ofJapanese Application No. 2017-135449, filed Jul. 11, 2017, thedisclosures of each of which are incorporated herein by reference intheir entirety.

TECHNICAL FIELD

The present invention relates to a sheet-like structure, a shapeestimation method, and a spacecraft.

BACKGROUND ART

A sheet-like member is used in a wide variety of uses in varioustechnical fields. For example, Non-Patent Literature 1 describes a solarsail, “IKAROS”. The solar sail is a space yacht including a sail thatreceives sunlight. The solar sail navigates in space by using, aspropulsion force, a radiation pressure that the sail receives from thesunlight.

The sail is configured by extending a sheet-like thin film in space. Theextended sail becomes a large-sized structure having an area ofapproximately 200 m². Such an enlargement of the area of a membranesurface that receives the sunlight increases a radiation pressure thatacts on the solar sail, and a propulsion force necessary to navigate isobtained.

CITATION LIST Non-Patent Literature

-   Non-Patent Literature 1: Osamu MORI, Junichiro KAWAGUCHI (et al.),    “Summary of Development and Operation of IKAROS”, Aeronautical and    Space Sciences Japan, Vol. 60, No. 8, pp. 283-289 (August 2012)

DISCLOSURE OF INVENTION Technical Problem

However, the sheet-like member has problems such as being easy todeflect. For example, in the solar sail described in Non-PatentLiterature 1, a radiation pressure corresponding to the shape of theextended sail acts on the extended sail. For example, in a state wherethe shape of the sail is different from an assumed shape due todeflection or the like of the sail, such a possibility that theradiation pressure acts in an unintentional direction and an attitude orthe like of the solar sail deviates is caused. For that reason, graspingthe shape of the extended sail is important.

For example, Non-Patent Literature 1 describes monitor cameras installedin a spacecraft main body and separation cameras that separate from thespacecraft main body. In the solar sail, images of the sail are capturedusing the monitor cameras and the separation cameras, and thus anextended state of the sail can be confirmed. However, in the method ofcapturing images of the sail using the cameras, a range available forimage-capturing, or the like is limited. This may make it difficult toaccurately grasp the shape such as unevenness of the sail.

In view of the circumstances described above, it is an object of thepresent invention to provide a sheet-like structure, a shape estimationmethod, and a spacecraft, which are capable of highly accuratelyestimating a sheet-like shape.

Solution to Problem

In order to achieve the object described above, according to anembodiment of the present invention, there is provided a sheet-likestructure including a sheet-like member and a plurality of detectionsensors.

The sheet-like member extends along an in-plane direction orthogonal toa thickness direction and receives light incident on the sheet-likemember.

The plurality of detection sensors are dispersedly arranged on thesheet-like member along the in-plane direction and are for detecting anincident angle of the light with respect to the sheet-like member ateach arrangement position of the plurality of detection sensors.

In the sheet-like structure, the plurality of detection sensors aredispersedly arranged on the sheet-like member, on which light isincident, along the in-plane direction of the sheet-like member. From adetection result of each detection sensor, an incident angle of thelight with respect to the sheet-like member at the arrangement positionof each detection sensor is detected. This allows a sheet-like shape tobe highly accurately estimated.

The light may include sunlight. In this case, the plurality of detectionsensors may include a thin-film solar cell.

For example, use of the thin-film solar cell allows an incident angle ofthe sunlight to be easily detected and allows the sheet-like shape to beeasily estimated.

The plurality of detection sensors may include a temperature sensor.

For example, use of the temperature sensor allows an incident angle ofthe light to be easily detected and allows the sheet-like shape to beeasily estimated.

According to an embodiment of the present invention, there is provided ashape estimation method including setting a reference plane of asheet-like structure on which light is incident.

First information regarding an incident direction of the light withrespect to the reference plane is acquired.

Second information regarding incident angles of the light with respectto the sheet-like structure at a plurality of detection positions isacquired in two or more states in which the incident directions aredifferent from one another, the plurality of detection positions beingdispersedly arranged on the sheet-like structure.

A shape of the sheet-like structure is estimated on the basis of thefirst information and the second information in the two or more states.

In the shape estimation method, the first information regarding anincident direction of the light with respect to the reference plane ofthe sheet-like structure, and the second information regarding incidentangles of the light with respect to the sheet-like structure at aplurality of detection positions are acquired. Using the firstinformation and the second information acquired in two or more states inwhich the incident directions with respect to the reference plane aredifferent from one another, a sheet-like shape can be highly accuratelyestimated.

In the shape estimation method, a position in an orthogonal directionorthogonal to the reference plane may be estimated for each of theplurality of detection positions of the sheet-like structure, toestimate the shape of the sheet-like structure.

This allows the shape of the sheet-like structure to be estimated from acomponent in a direction orthogonal to the reference plane. As a result,the amount of operation for shape estimation, or the like is suppressed,and an operation speed is improved.

In the shape estimation method, the shape of the sheet-like structuremay be monitored.

This allows the shape of the sheet-like structure to be monitored inreal time, for example.

According to an embodiment of the present invention, there is provided aspacecraft including a sheet-like structure and a main body connected tothe sheet-like structure.

The sheet-like structure includes a sheet-like member and a plurality ofdetection sensors. The sheet-like member extends along an in-planedirection orthogonal to a thickness direction and receives lightincident on the sheet-like member.

The plurality of detection sensors are dispersedly arranged on thesheet-like member along the in-plane direction and are for detecting anincident angle of the light with respect to the sheet-like member ateach arrangement position of the plurality of detection sensors.

The light may include sunlight. In this case, the main body may includea sun sensor that detects an incident direction of the sunlight.

Advantageous Effects of Invention

According to the present invention, it is possible to provide asheet-like structure, a shape estimation method, and a spacecraft, whichare capable of highly accurately estimating a sheet-like shape.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a perspective view of a spacecraft including a sail accordingto an embodiment of the present invention.

FIG. 2 is a schematic view of a configuration example of a thin-filmsolar cell.

FIG. 3 is a graph showing a relationship between a voltage output and anincident angle β of the thin-film solar cell.

FIG. 4 is a schematic view of the sail extended on a plane.

FIG. 5 is a schematic view of a configuration example of a temperaturesensor.

FIG. 6A is a schematic view of a configuration example of a gossamerstructure.

FIG. 6B is a schematic view a configuration example of a gossamerstructure.

MODE(S) FOR CARRYING OUT THE INVENTION

Hereinafter, a solar sail, which is an example of a sheet-likestructure, will be described as an embodiment of the present inventionwith reference to the drawings. Further, light will be described assunlight. It should be noted that the present invention is not construedas limiting by the following embodiment.

1. Configuration of Sail

FIG. 1 is a perspective view of a spacecraft 100 including a sail 10according to an embodiment of the present invention. As shown in FIG. 1, the spacecraft 100 includes the sail 10 and a spacecraft main body 20.The spacecraft 100 is a solar sail that navigates in space, extendingthe sail 10. In this embodiment, the sail 10 corresponds to a sheet-likestructure.

As shown in FIG. 1 , the sail 10 includes a sheet-like member 11 and aplurality of detection sensors 12. The sheet-like member 11 has asheet-like shape extending along an in-plane direction orthogonal to athickness direction and having flexibility. Thus, the sheet-like member11 has a thin and wide surface capable of being easily bent. FIG. 1schematically illustrates deflection of the sheet-like member 11 or asolid shape such as unevenness by using dotted lines.

The sheet-like member 11 includes a front surface 13, a back surface 14,and an aperture 15. The front surface 13 is a surface, which is directedtoward the sun and on which sunlight 30 is incident. It should be notedthat FIG. 1 schematically illustrates the sunlight 30 incident on thefront surface 13 by using arrows.

The back surface 14 is a surface opposite to the side, of the sheet-likemember 11, on which the sunlight 30 is incident. Thus, the thicknessdirection of the sheet-like member 11 is a direction orthogonal to thefront surface 13 and the back surface 14, and the in-plane direction isa direction along the front surface 13 and the back surface 14. Theaperture 15 is arranged at the center of the sheet-like member 11. Inthe aperture 15, the spacecraft main body 20 is installed.

In a case where the sheet-like member 11 is extended on a plane, theplanar shape of the sheet-like member 11 is a substantially square (seeFIG. 4 ). The length of one side of the square is set to, for example,approximately 14 m. In this case, the area of the square isapproximately 200 m². Further, the thickness of the sheet-like member 11is set to several micrometers. With this configuration, it is possibleto achieve a sail 10 that is lightweight while having a large-sizedstructure. The present invention is applicable irrespective of theplanar shape, the size, the thickness, and the like of the sheet-likemember 11.

For the sheet-like member 11, for example, a thin film made of polyimideresin or the like, which is capable of extending in a space environment,is used. Further, aluminum is vapor-deposited on the sheet-like member11, and such a sheet-like member 11 is capable of reflecting thesunlight 30. With this configuration, the sheet-like member 11 iscapable of efficiently receiving a radiation pressure due to thesunlight 30 and is capable of producing a sufficient propulsion force.The specific configuration of the sheet-like member 11 is not limited.For example, an optional configuration capable of receiving a radiationpressure due to the sunlight 30 may be used.

The plurality of detection sensors 12 are each a sensor for detecting anincident angle of the sunlight 30 with respect to the sheet-like member11. The plurality of detection sensors 12 are dispersedly arranged onthe front surface 13 of the sheet-like member 11 along the front surface13. For example, the plurality of detection sensors 12 are dispersedlyarranged at predetermined intervals such that the density of the sensorsis balanced. As a matter of course, in accordance with the configurationof the sheet-like member 11 or the like, an arrangement position of eachdetection sensor 12, or the like may be appropriately set.

In this embodiment, a thin-film solar cell is used for the detectionsensor 12. The thin-film solar cell is configured using, for example, anamorphous silicon (a-Si) cell having a thickness of several tens ofmicrometers. Using such a thin element allows the load on the sheet-likemember 11 or the like to be sufficiently suppressed and, for example,allows the sheet-like member 11 to be suitably extended.

FIG. 2 is a schematic view of a configuration example of a thin-filmsolar cell 40. The thin-film solar cell 40 (detection sensor 12)includes an incident surface 41 on which the sunlight 30 is incident,and a rear surface 42 opposite to the incident surface 41. The thin-filmsolar cell 40 is configured such that the incident surface 41 and therear surface 42 are substantially parallel to each other. The thin-filmsolar cell 40 is arranged at an arrangement position P (black circle inthe figure) with the rear surface 42 facing the front surface 13 of thesheet-like member 11.

At the arrangement position P, the direction orthogonal to the incidentsurface 41 of the thin-film solar cell 40 and the direction orthogonalto the front surface 13 of the sheet-like member 11 are substantiallythe same direction. In other words, the normal direction of the incidentsurface 41 of the thin-film solar cell 40 is substantially parallel tothe normal direction of the front surface 13 of the sheet-like member 11at the arrangement position P. FIG. 2 shows, using a local normal vectorn, the normal direction of the front surface 13 of the sheet-like member11 at the arrangement position P.

As shown in FIG. 2 , an incident angle of the sunlight 30 with respectto the sheet-like member 11 at the arrangement position P is an angledefined by the local normal vector n and a sun vector S at thearrangement position P. Here, the sun vector S is a unit vectorrepresenting a direction toward the sun when the sun is viewed from thearrangement position P. Thus, the sunlight 30 is incident along thedirection parallel to the sun vector S.

The sunlight 30 is incident on the incident surface 41 of the thin-filmsolar cell 40, which is arranged at the arrangement position P, at anangle substantially equal to the incident angle of the sunlight 30 withrespect to the sheet-like member 11 at the arrangement position P.

Hereinafter, the incident angles of the sunlight 30 incident on thesheet-like member 11 and the thin-film solar cell 40 will be describedas an incident angle β by using the same reference symbol β.

FIG. 3 is a graph showing a relationship between a voltage output andthe incident angle β of the thin-film solar cell 40. The horizontal axisof FIG. 3 is the incident angle β with respect to the incident surface41 of the thin-film solar cell 40. Further, the vertical axis is avoltage V, which is output from the thin-film solar cell 40.

A voltage V corresponding to the incident angle β is output from thethin-film solar cell 40. Specifically, the voltage V of the thin-filmsolar cell 40 takes a value proportional to cos(β). Thus, as shown inFIG. 3 , in a case where the sunlight 30 is incident from a direction(β=0°) orthogonal to the thin-film solar cell 40, the voltage V ismaximum. Further, in a case where the sunlight 30 is incident from adirection (β=90°) parallel to the thin-film solar cell 40, the voltage Vis zero.

For example, the relationship between the voltage V, which is outputfrom the thin-film solar cell 40, and the incident angle β is measuredand stored in advance. Referring to the relationship between the voltageV and the incident angle β, the incident angle β of the sunlight 30incident on the thin-film solar cell 40 can be detected from the voltageV (∝ cos(β)) of the thin-film solar cell 40. In other words, theincident angle β of the sunlight 30 with respect to the sheet-likemember 11 at the arrangement position P can be detected from the voltageV of the thin-film solar cell 40.

As shown in FIG. 1 , the spacecraft main body 20 has a columnar shapeextending along the center axis 21. The spacecraft main body 20 isarranged at the aperture 15 of the sail 10. The spacecraft main body 20and the sail 10 are mechanically and electrically connected to eachother via tethers and harnesses not shown in the figure. The spacecraftmain body 20 includes a sun sensor, an attitude control mechanism, and ashape estimation processing unit (each of which is not illustrated).

The sun sensor (light sensor) detects an incident direction of thesunlight 30. In other words, the sun sensor detects a direction towardthe sun when the sun is viewed from the spacecraft. A specificconfiguration of the sun sensor or the like is not limited and, forexample, an optional sensor capable of detecting the incident directionof the sunlight 30 may be used.

The attitude control mechanism includes a thruster for controlling theattitude of the spacecraft, or the like. The spacecraft main body 20 iscapable of performing rotary motion with the center axis 21 being as areference by using the attitude control mechanism. In the spacecraft100, the large sail 10 is deployed and extended using a centrifugalforce generated by the rotary motion. Thus, the spacecraft 100 navigatesin space, with the sail 10 being extended, while rotating with thecenter axis 21 being as the reference and.

The shape estimation processing unit acquires outputs from the pluralityof detection sensors 12 and the sun sensor. The shape estimationprocessing unit is capable of executing the processing of estimating theshape of the sail 10, which will be described later, or the like on thebasis of the acquired data. Further, the shape estimation processingunit may perform communication with a control system on the ground orthe like via a communication antenna.

For the shape estimation processing unit, for example, a computer can beused. The operation of each unit of the spacecraft 100 may beappropriately controlled by the computer.

FIG. 4 is a schematic view of the sail 10 extended on a plane. FIG. 4shows the sail 10 (sheet-like member 11) two-dimensionally extendedalong a plane orthogonal to the center axis 21 of the spacecraft mainbody 20. A plane including the two-dimensionally extended sail 10 is setto a reference plane 16 of the sail 10. In other words, a plane on whichthe sail 10 is two-dimensionally extended so as to be orthogonal to thecenter axis 21 of the spacecraft main body 20 is set to the referenceplane 16. It should be noted that the method of setting the referenceplane 16 or the like is not limited, and the reference plane 16 may beappropriately set according to the configuration of the sail 10 or thelike.

In the spacecraft 100, the X-axis, the Y-axis, and the Z-axis orthogonalto one another are set with a point, at which the center axis 21 of thespacecraft main body 20 and the reference plane 16 intersects with eachother, being as the origin O. In other words, the axes are set such thatthe XY-plane becomes the reference plane 16, and a direction parallel tothe Z-axis becomes a direction orthogonal to the reference plane 16. Itshould be noted that the method of setting the reference plane 16, theorigin O of the X-, Y-, and Z-axes, or the like is not limited and maybe appropriately set according to the configuration of the sail 10 orthe like.

As described above, the sun sensor detects the incident direction of thesunlight 30. In this embodiment, the sun sensor detects a sun vectorS=(s_(x), s_(y), s_(z))^(T) on the XYZ coordinates set on the referenceplane 16 of the sail 10. Here, the superscript “T” represents thetransposition of the vector.

As shown in FIG. 4 , the sun vector S can be represented using theincident angle of the sunlight 30 with respect to the reference plane 16(reference incident angle βb) and an azimuthal angle Φ. The referenceincident angle βb is an angle defined by a reference normal vector nb,which represents a normal direction of the reference plane 16, and thesun vector S. Further, the azimuthal angle Φ is an angle defined by acomponent, of the sun vector S, which is parallel to the reference plane16, and the X-axis, and is also an angle representing the azimuthdirection of the sun vector S on the XY-plane.

The sun sensor detects, for example, the reference incident angle βb andthe azimuthal angle Φ of the sunlight 30 to detect the sun vector S. Asa matter of course, XYZ components of the sun vector S may be directlydetected. In addition to the above, an optional method capable ofdetecting the incident direction of the sunlight 30 with respect to thereference plane 16 may be used. In this embodiment, the referenceincident angle βb and the azimuthal angle Φ are included in firstinformation regarding the incident direction of the sunlight 30 withrespect to the reference plane.

In general, a distance between the sun and the spacecraft 100 issufficiently large. So, the sunlight 30 incident on the sail 10 can beconsidered to be substantially parallel light. Thus, the sun vector S isconstant irrespective of the position of the sail 10.

Meanwhile, in the actual spacecraft 100, the shape of the sail 10includes three-dimensionally unevenness such as deflection as shown inFIG. 1 . Thus, the normal direction at each position of the sail 10 isdirected toward a direction corresponding to the shape of the sail 10.

FIG. 4 schematically shows a partial region 17 in a case where the sail10 has a three-dimensional shape, and a local normal vector n in thepartial region 17. An incident angle β of the sunlight 30 incident onthe partial region 17 is an angle defined by the local normal vector nand the sun vector S. Thus, the incident angle β in the partial region17 is an angle corresponding to the orientation of the local normalvector n.

As described above, the incident angle β of the sunlight 30 with respectto the sail 10 (sheet-like member 11) at each position on the sail 10 isan angle corresponding to the shape at each position. Hereinafter, theincident angle β at each position will be described as a local incidentangle β.

As described above, an output of the detection sensor 12 arranged ateach arrangement position P on the sail 10 (the voltage V of thethin-film solar cell 40) is acquired, and thus the local incident angleβ at each arrangement position P is detected. In this embodiment, theoutputs from the plurality of detection sensors 12 are included insecond information regarding the incident angles of the sunlight withrespect to the sheet-like structure at a plurality of detectionpositions dispersedly arranged on the sheet-like structure.

2. Shape Estimation of Sail 10

In this embodiment, the shape of the sail 10 is expressed using an XYZcoordinate system with the reference plane 16 of the sail 10 being as areference. Hereinafter, it is assumed that the deformation of the sail10 in the in-plane direction can be ignored. Thus, a deformation in adirection (Z-axis direction) orthogonal to the in-plane direction of thesail 10 is estimated, and the shape of the sail 10 is thus estimated.Hereinafter, the length of a side of the square-shaped sail will bedescribed as L.

An optional point r on the incident surface 41 on the sail 10(sheet-like member 11) is represented as r=(x, y, z)^(T) using the XYZcoordinate system. Using a patch of the Monge form, the point r isrewritten as follows.

$\begin{matrix}\left\lbrack {{Math}.1} \right\rbrack &  \\{{{r\left( {\xi,\eta} \right)} = {\begin{pmatrix}x \\y \\z\end{pmatrix} \equiv \begin{pmatrix}\xi \\\eta \\{z\left( {\xi,\eta} \right)}\end{pmatrix}}},{\left( {\xi,\eta} \right) \in {\left\lbrack {{- 1},1} \right\rbrack \times \left\lbrack {{- 1},1} \right\rbrack}}} & (1)\end{matrix}$

Here, ξ and η are parameters respectively corresponding to an Xcomponent and a Y component of the point r. It should be noted that ξand η are values normalized by half the length (L/2) of the side L ofthe sail 10 and are each set to a value from −1 to 1. In the Monge form,as shown in Expression (1), z, which is a Z component of the point r, isreplaced with z(ξ, η) as a function of ξ and η. Thus, the point r on thesail 10 can be considered to be a function r(ξ, η) of ξ and η.

In the replacement shown in Expression (1), that is, the parametricpresentation from r(x, y, z) to r(ξ, η), partial derivatives for rregarding ξ and η have a linear independent relationship. Specifically,the partial derivatives for r using the parameters ξ and η are expressedas follows.

$\begin{matrix}\left\lbrack {{Math}.2} \right\rbrack &  \\{{r_{\xi} = {\frac{\partial r}{\partial\xi} = \begin{pmatrix}1 \\0 \\\frac{\partial z}{\partial\xi}\end{pmatrix}}},{r_{\eta} = {\frac{\partial r}{\partial\eta} = \begin{pmatrix}0 \\1 \\\frac{\partial z}{\partial\eta}\end{pmatrix}}}} & (2)\end{matrix}$

Partial derivatives r_(ξ) and r_(η) for r represent vectors parallel toa plane being in contact with the sail 10 at the point r (tangentplane). The direction orthogonal to the tangent plane is a normaldirection at the point r. Thus, a local normal vector n at the point ris expressed as follows using a vector product (r_(ξ)×r_(η)) of thepartial derivatives r_(ξ) and r_(η) for r.

$\begin{matrix}\left\lbrack {{Math}.3} \right\rbrack &  \\{n = {\frac{r_{\xi} \times r_{\eta}}{{r_{\xi} \times r_{\eta}}} = \frac{\left( {{- \frac{\partial z}{\partial\xi}},{- \frac{\partial z}{\partial\eta}},1} \right)^{\top}}{\sqrt{1 + \left( \frac{\partial z}{\partial\xi} \right)^{2} + \left( \frac{\partial z}{\partial\eta} \right)^{2}}}}} & (3)\end{matrix}$

As shown in Expression (3), the local normal vector n is a unit vectornormalized by an absolute value of the vector product, ∥r_(ξ)×r_(η)∥.Further, the local normal vector n is expressed using a partialderivative of z(ξ, η) regarding ξ and η.

For the Z component (z(ξ, η)) of the sail 10, power series expansionregarding ξ and η will be considered. When the center r(0, 0) of thesail 10 is set as a reference and expanded as infinite series, z(ξ, η)is expressed by the following expression.

$\begin{matrix}\left\lbrack {{Math}.4} \right\rbrack &  \\{{z\left( {\xi,\eta} \right)} = {\sum\limits_{k = 0}^{\infty}{\sum\limits_{\ell = 0}^{k}{{\overset{\sim}{a}}_{k\ell}\frac{1}{k!}\begin{pmatrix}k \\\ell\end{pmatrix}\xi^{k}\eta^{\ell - k}}}}} & (4)\end{matrix}$

It should be noted that “0” in the right side of Expression (4)represents a binomial coefficient and represents, for example, acoefficient of the term α¹ in the expansion of (1+α)^(k). A maximumvalue k_(max) of a degree expanded in Expression (4) can be set to roundoff a degree larger than k_(max). The method of setting the maximumvalue k_(max) or the like is not limited. For example, the maximum valuek_(max) may be appropriately set according to requested calculationaccuracy or the like. If the sum in the Expression (4) is rewritten andan expansion coefficient is defined again, the Z component z(ξ, η) ofthe sail 10 is expressed as follows.

$\begin{matrix}\left\lbrack {{Math}.5} \right\rbrack &  \\{{{z\left( {\xi,\eta} \right)} \simeq {\sum\limits_{k = 0}^{k_{\max}}{{h_{k}\left( {\xi,\eta} \right)}a_{k}}}} = {{h^{\top}\left( {\xi,\eta} \right)}a}} & (5)\end{matrix}$

As shown in Expression (5), z(ξ, η) can be expressed using an innerproduct h^(T)(ξ, η)a of a vector h^(T)(ξ, η) regarding ξ and η and avector a regarding an expansion coefficient a_(k). It should be notedthat the vector h^(T)(ξ, η) is specifically expressed by the followingexpression.

[Math. 6]

h(ξ,η)=(1,ξ,η,ξ²,2ξη,η²,ξ³,3ξ²η,3ξη², . . . )^(T)   (6)

Using Expression (5) in such a manner, the shape of the sail 10 (Zcomponent of the point r) can be expressed by the expansion coefficient,the vector a=(a₀, a₁, a₂, a₃, . . . )^(T). In other words, specificallycalculating the expansion coefficient a allows the shape of the sail 10to be estimated.

As described above, Expression (3) expressing the local normal vector ncan be expressed using the partial derivatives of z(ξ, η) regarding ξand η. For example, it is assumed that z(ξ, η) shown in Expression (5)is subjected to partial differentiation to express the local normalvector n. In this case, the partial derivatives of z(ξ, η) regarding ξand η can be expressed in a simple form as follows.

$\begin{matrix}\left\lbrack {{Math}.7} \right\rbrack &  \\{{\frac{\partial z}{\partial\xi} = {h_{\xi}^{\top}a}},{\frac{\partial z}{\partial\eta} = {h_{\eta}^{\top}a}}} & (7)\end{matrix}$

Here, h_(ξ) ^(T) and h_(η) ^(T) express partial derivatives of h^(T)(ξ,η) regarding ξ and η. h_(ξ) ^(T) and h_(η) ^(T) are specificallyexpressed by the following expression.

$\begin{matrix}\left\lbrack {{Math}.8} \right\rbrack &  \\{h_{\xi} = {\frac{\partial h}{\partial\xi} = \left( {0,1,0,{2\xi},{2\eta},0,{3\xi^{2}},{6{\xi\eta}},{3\eta^{2}},\ldots} \right)^{\top}}} & (8)\end{matrix}$ $\begin{matrix}\left\lbrack {{Math}.9} \right\rbrack &  \\{h_{\eta} = {\frac{\partial h}{\partial\eta} = \left( {0,0,1,0,{2\xi},{2\eta},0,{3\xi^{2}},{6{\xi\eta}},\ldots} \right)^{\top}}} & (9)\end{matrix}$

Thus, the partial derivatives of z(ξ, η) regarding ξ and η shown inExpression (7) are substituted in Expression (3), and thus the localnormal vector n can be expressed in the form including the expansioncoefficient a. Further, using the local normal vector n, the localincident angle β of the sunlight 30 with respect to the sail 10, thesunlight 30 being incident on an optional point on the sail 10, can beexpressed.

As described with reference to FIG. 4 , the local incident angle β ofthe sunlight 30 at the point r(x, y)=r(x(ξ, y(η)) on the sail 10 is anangle between the sun vector S and the local normal vector n at thepoint r. An inner product of the local normal vector n and the sunvector S is n·S=|n∥S|cos(β). Since the local normal vector n and the sunvector S are unit vectors, the magnitude of each vector is 1. Thus,n·S=cos(β).

A cosine of the local incident angle β of the sunlight 30, that is, cos(β), is expressed by the following expression using the local normalvector n shown in Expression (3) and the sun vector S=(s_(x), s_(y),s_(z))^(T).

$\begin{matrix}\left\lbrack {{Math}.10} \right\rbrack &  \\{{\cos\beta} = {{n \cdot s} = \frac{s_{z} - {s_{x}h_{\xi}^{\top}a} - {s_{y}h_{\eta}^{\top}a}}{\sqrt{1 + \left( {h_{\xi}^{\top}a} \right)^{2} + \left( {h_{\eta}^{\top}a} \right)^{2}}}}} & (10)\end{matrix}$

As shown in Expression (10), cos(β) is a function of the expansioncoefficient a and the sun vector S. In other words, the local incidentangle β at each point on the sail 10 is expressed as a functionincluding the expansion coefficient a. It should be noted that aposition at which the sunlight 30 is incident is expressed by ξ and η.

As described above, in the spacecraft 100, the sun vector S and thelocal incident angle β(cos(β)) at each arrangement position of theplurality of detection sensors 12 are detected. Hereinafter, anarrangement position at which each detection sensor 12 is arranged willbe described as P_(i)(x_(i), y_(i)). Here, a subscript i is an integerto be i=1 . . . N, and is an index that indicates each detection sensor.N is the total number of the detection sensors 12 arranged on the sail10. Further, in order to distinguish from the local incident angle βshown in Expression (10), an incident angle of the sunlight 30 detectedby the i-th detection sensor 12 will be described as a local incidentangle βi* using “*”.

The expansion coefficient a is determined such that a difference betweencos(βi) shown in Expression (10) and an actually detected cos(βi*) isminimum. In other words, the expansion coefficient a=(a₀, a₁, a₂, a₃, .. . )^(T) is determined so as to achieve Pi having a minimum errorbetween βi and βi*, which is the detected value.

In this embodiment, in order to obtain the expansion coefficient a, theleast squares method regarding cos(βi) and cos(βi*) at the arrangementposition P_(i) of each detection sensor is executed. Specifically, theprocessing of minimizing the following expression is executed.

$\begin{matrix}\left\lbrack {{Math}.11} \right\rbrack &  \\{{minimize}{\sum\limits_{i = 1}^{N}\left( {{\cos{\beta_{i}(a)}} - {\cos\beta_{i}^{*}}} \right)^{2}}} & (11)\end{matrix}$

Expression (11) is an expression for calculating the sum of squares of adifference between cos βi(a), which is a function of the expansioncoefficient a, and cos(βi*), which is the detected value, at all thedetection sensors 12. In the minimizing processing, the expansioncoefficient a is determined such that the sum is minimum. It should benoted that as shown in Expression (10), cos βi(a) is a non-linearfunction with respect to the expansion coefficient a. Thus, theminimizing processing is processing of handling a non-linear leastsquares method.

A specific method for the minimizing processing or the like is notlimited. For example, in a case where a displacement of the sail 10 inthe Z-axis direction (z(ξ, η)) is sufficiently small and the area of thesail 10 is sufficiently large, it is possible to approximate cos β(a) asa linear function with respect to the expansion coefficient a. Usingthis approximation, the minimizing processing becomes the processing ofhandling a linear least squares method. As a result, for example, theexpansion coefficient a can be analytically calculated, and time forcalculation processing can be sufficiently shortened. In addition to theabove, an optional method capable of calculating the expansioncoefficient a may be appropriately used.

Using data obtained when the sunlight 30 is incident in differentdirections, the expansion coefficient a can be solved. In other words,the minimizing processing is performed by using the sun vector S and thelocal incident angle βi* at each position, in a state where the sunvectors S are different from one another, and thus the expansioncoefficient a can be properly calculated.

In this embodiment, in two or more states where the sun vectors S of thesunlight 30 with respect to the reference plane 16 are different fromone another, information regarding the local incident angle βi* of thesunlight 30 with respect to the sail 10 at the arrangement position ofeach of the plurality of detection sensors 12 dispersedly arranged onthe sail 10 is acquired. Subsequently, on the basis of the informationregarding the sun vectors S in the two or more states and theinformation regarding the local incident angle βi*, the shape of thesail 10 is estimated.

For example, the spacecraft 100 extends the sail 10 by rotary motion.For that reason, the direction of the sun when viewed from the referenceplane 16 of the sail 10, that is, the sun vector S in the XYZ coordinatesystem fixed to the spacecraft main body 20 changes over time.

In the spacecraft 100, the sun vector S and the local incident angle βi*at each position are acquired at, for example, a predetermined samplingrate. In other words, a data set including the sun vector S and thelocal incident angle βi* is sequentially acquired at different timings.It should be noted that while the data sets are being acquired at therespective timings, the change in the shape of the sail 10 can beignored.

Hereinafter, in order to distinguish the data sets acquired at apredetermined sampling rate from one another, an index j (j=1 to M) isused. For example, the sun vectors S and the local incident angles βi*,which are acquired at different timings j, are described as follows.

[Math. 12]

s ^(j)=(s _(x) ^(j) ,s _(y) ^(j) ,s _(z) ^(j))^(T)

cos β_(i) ^(j)*

In this embodiment, using the data sets acquired at different timings j,the minimizing processing is executed on the basis of Expression (11).Specifically, the expression to be minimized is expressed as follows.

$\begin{matrix}\left\lbrack {{Math}.13} \right\rbrack &  \\{{minimize}{\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{M}\left( {{\cos{\beta_{i}^{j}(a)}} - {\cos\beta_{i}^{j*}}} \right)^{2}}}} & (12)\end{matrix}$

In Expression (12), the data set is acquired at least twice. In otherwords, the number of times M, by which the data set is acquired, isappropriately set to M≥2. Increasing the number of times M allows thecalculation accuracy of the expansion coefficient a to be improved, forexample. Alternatively, reducing the number of times M allows time,power, or the like for the minimizing processing to be suppressed.

Further, as described above, it is assumed that the shape of the sail 10does not change while the data set is being acquired at each timing j.In other words, the expansion coefficient a representing the shape ofthe sail 10 is constant irrespective of the timing at which each dataset is acquired.

The minimizing processing for Expression (12) is executed, and theexpansion coefficient a is calculated. The calculated expansioncoefficient a is substituted in Expression (5), and thus a position z(ξ,η) of the sail 10 in the Z-axis direction at the arrangement positionP_(i) of each detection sensor 12 is calculated. From z(ξ, η) at eacharrangement position P_(i), a three-dimensional shape includingunevenness or the like of the sail 10 is estimated. This allows asheet-like shape to be highly accurately estimated.

In such a manner, in this embodiment, the position z(ξ, η) in theorthogonal direction orthogonal to the reference plane 16 is estimatedfor each of the plurality of arrangement positions P, of the sail 10,and thus the shape of the sail 10 is estimated. This allows the shape ofthe sail 10 to be easily estimated, for example, without calculating thecomponents in the X-axis direction and the Y-axis direction, or thelike. As a result, the amount of operation for shape estimation or thelike can be suppressed, and an operation speed or the like can beimproved.

For example, when a simulation for the shape estimation was performed onthe sail 10 having the size of 50 m×50 m by using the shape estimationmethod according to the present invention, a maximum estimation errorwas approximately 0.1 m. In such a manner, the shape can also beestimated with sufficiently high accuracy for a large-sized sheet-likestructure.

In the spacecraft 100, for example, the shape estimation processing unit(computer) mounted to the spacecraft main body 20 acquires informationsuch as the sun vector S and the local incident angle β. The shapeestimation processing unit calculates the shape of the sail 10, forexample, at predetermined intervals on the basis of the acquiredinformation.

The calculated data is transmitted to the control system on the groundor the like. In the control system, for example, the shape of the sail10 is visualized and monitored. This allows the shape of the sail 10 tobe monitored in real time. As a result, for example, it is possible tomake a flight plan on the basis of information such as the shape of thesail 10.

It should be noted that the present invention is not limited to the casewhere the shape estimation processing unit mounted to the spacecraftmain body 20 executes the processing of estimating the shape of the sail10, and the shape of the sail 10 may be estimated by another system orthe like. For example, information such as the sun vector S and thelocal incident angle β may be transmitted to the ground by thespacecraft 100, and the processing of estimating the shape of the sail10 may be executed by a system on the ground. This can suppress thepower consumption of the spacecraft 100, which is involved with theprocessing of estimating the shape or the like.

Further, the method of acquiring the information regarding the sunvector S is not limited to the method using the sun sensor. For example,the sun vector S may be calculated on the basis of information such asan orbit, an attitude, or a position of the spacecraft 100. In thiscase, information regarding the calculated sun vector S is appropriatelytransmitted to a computer that performs the processing of estimating theshape, or the like. With this configuration, for example, even in a casewhere the sun sensor is not mounted to the spacecraft main body 20, theshape of the sail 10 can be easily estimated.

In the above description, the thin-film solar cell 40 is used as thedetection sensor 12 for detecting the local incident angle β of thesunlight 30. In the present invention, a temperature sensor can also beused as the detection sensor 12.

FIG. 5 is a schematic view of a configuration example of a temperaturesensor 50. The temperature sensor 50 (detection sensor 12) includes asensor plate 51, a temperature detection element 52, and a cover film53. The sensor plate 51 has a flat plate-like shape and is arrangedalong the in-plane direction of the sail 10 (sheet-like member 11). Forthe sensor plate 51, for example, a member having high heat conductivityis used.

The temperature detection element 52 is thermally connected to thesensor plate 51 and detects the temperature of the sensor plate 51. Forexample, as shown in FIG. 5 , the temperature detection element 52 isembedded in the sensor plate 51. For the temperature detection element52, for example, a resistive element (resistance thermometer) whoseresistivity changes according to the temperature, a thermocouple(thermocouple thermometer) that measures temperature using athermoelectromotive force, or the like is used. In addition to theabove, an optional element capable of measuring temperature may be usedas the temperature detection element.

The cover film 53 is arranged so as to cover the sensor plate 51installed on the sail 10 and fixes the sensor plate 51 and thetemperature detection element 52 to the sail 10.

FIG. 5 shows a temperature sensor 50 a arranged on the front surface 13of the sail 10, on which the sunlight 30 is incident, and a temperaturesensor 50 b installed on the back surface 14 of the sail 10. In such amanner, the temperature sensor 50 can be installed on both of the frontsurface 13 and the back surface 14 of the sail 10. For example, theplurality of temperature sensors 50 may be arranged on one of the frontsurface 13 and the back surface 14 of the sail 10 or may be installed onboth of the front surface 13 and the back surface 14 of the sail 10.

For example, it is assumed that optical characteristics such asabsorptivity of light or emissivity of light (infrared light) aredetermined for the members (sensor plate 51 and cover film 53)constituting the temperature sensor 50. In this case, a temperatureT_(sensor) detected by the temperature sensor 50 has a valuecorresponding to the local incident angle β of the sunlight 30.

For example, when the sunlight 30 is incident on the sensor plate 51,part of the sunlight 30 is absorbed and the temperature of the sensorplate 51 rises. At that time, the amount of heat absorbed by the sensorplate 51 is proportional to cos(β). Meanwhile, the amount of heat isreleased (radiated) from the sensor plate 51 to the space via the frontsurface 13 and the back surface 14 of the sail 10. The balance of theamount of heat in the sensor plate 51 is calculated in such a manner,and thus the local incident angle β can be obtained from the temperatureT_(sensor) detected by the temperature sensor 50.

In such a manner, also in a case where the temperature sensor 50 isused, it is possible to acquire information regarding the local incidentangle β of the sunlight 30 with respect to the sail 10 at eacharrangement position of the plurality of temperature sensors 50dispersedly arranged on the sail 10. This allows the shape of the sail10 to be highly accurately estimated.

It should be noted that the present invention is not limited to a casewhere one of the thin-film solar cell 40 and the temperature sensor 50is used as the detection sensor 12. For example, both the thin-filmsolar cell 40 and the temperature sensor 50 may be appropriately used asthe detection sensors 12. In this case, the degree of freedom indesigning the sail 10 or the like can be improved.

Hereinabove, in the sail 10 according to this embodiment, the pluralityof detection sensors 12 are dispersedly arranged on the sheet-likemember 11, on which the sunlight 30 is incident, along the in-planedirection of the sheet-like member 11. From the detection result of eachdetection sensor 12, the local incident angle θ of the sunlight 30 withrespect to the sheet-like member 11 is detected at the arrangementposition of each detection sensor 12. This allows the sheet-like shapeto be highly accurately estimated.

In the sail 10 according to this embodiment, the local incident angle θof the sunlight 30 with respect to the sail 10 at each point is detectedby the detection sensor 12 arranged at each point on the sail 10. Insuch a manner, the angles of the sunlight incident on the respectivepoints are dispersedly measured, and thus information necessary toestimate the shape of the sail 10 at a desired accuracy can be easilyacquired.

For example, in a case where the spacecraft 100 (sail 10) is a solarpower sail configured to perform photovoltaic generation, cells(thin-film solar cells) or the like used for photovoltaic generation canbe used as the detection sensors 12 as they are. So, the shape of thesail 10 can be easily estimated without substantially increasing theweight of the spacecraft main body 20, or the like.

Further, in this embodiment, the information items regarding the sunvector S and the local incident angle β are detected in two or morestates where the sun vectors S are different from one another. Usingthose information items, an error when the shape of the sail 10 isestimated or the like can be sufficiently reduced. As a result, theshape of the sail 10 can be estimated with a sufficiently high accuracy.

The shape of the sail 10 is estimated by calculating a componentorthogonal to the reference plane 16 at each point. In other words, theprocessing of calculating the Z component among the three-dimensionalcomponents representing the respective points is executed. This allowsthe shape estimation for the sail 10 to be executed at high speed.Further, since a calculation load is small, mounting capable of on-boardprocessing allows the calculation to be easily automated.

It should be noted that the information regarding the sun vector S andthe local incident angle β, the information regarding the shape of thesail 10, or the like has a size sufficiently smaller than, for example,the size of image data or the like. Thus, those information items can beeasily transferred. As a result, the shape of the sail 10 can be easilymonitored in real time.

In such a manner, the shape of the sail 10 is highly accuratelyestimated, and thus an action of a radiation pressure, which is receivedby the sail 10, on the motion of the spacecraft 100, or the like can beinvestigated in detail. For example, an influence of the shape of thesail 10 on a rotation or an attitude of the spacecraft 100 (solar sail),or the like can be investigated in detail on the basis of an actualmeasurement result. Further, in a case where an adjustment mechanismthat adjusts the shape of the sail 10, or the like is mounted, estimatedshape data can be fed back to highly accurately adjust the shape of thesail 10.

3. Other Sheet-Like Structures

In the above description, the solar sail has been described as anexample of a large-sized structure (sheet-like structure) having asheet-shaped structure. A huge structure constituted by such asheet-like member (thin film, mesh, or the like) having flexibility isreferred to as a gossamer structure. Hereinafter, a gossamer structuredifferent from the sail 10 will be described.

FIG. 6A is a schematic view of an example of a gossamer structure 200including a concave front surface 213, on which the sunlight 30 isincident. FIG. 6B is a schematic view of an example of a gossamerstructure 300 including a convex front surface 313, on which thesunlight 30 is incident. It should be noted that the present inventionis applicable irrespective of the size, the shape, or the like of thegossamer structures 200 and 300.

As shown in FIG. 6A, if a huge sheet-like structure (gossamer structure200) including the concave front surface 213 is constituted, forexample, an electromagnetic wave or the like incident on the frontsurface 213 can be collected at a predetermined point. For example, theconcave front surface 213 is configured to be capable of reflecting thesunlight 30, thus achieving a condensing apparatus that condenses thesunlight 30. Further, the concave front surface 213 is configured to becapable of reflecting an electromagnetic wave having a predeterminedfrequency, thus achieving a huge antenna, radio telescope, or the like.

The detection sensors 12 (thin-film solar cells 40, temperature sensors50, or the like) are dispersedly arranged on such a gossamer structure200, and thus the shape of the gossamer structure 200 can be easilyestimated. FIG. 6A illustrates the detection sensors 12 dispersedlyarranged on the front surface 213. It should be noted that in a casewhere the detection sensors 12 are the temperature sensors 50, thedetection sensors 12 may be arranged on a back surface 214 opposite tothe front surface 213.

For example, a condensing efficiency of the condensing apparatus, adetection accuracy of the antenna (radio telescope), and the like can beinvestigated in detail on the basis of the estimated shape. Further, ina case where the shape of the gossamer structure 200 or the like isadjustable, the shape estimation enables highly accurate adjustment.

As shown in FIG. 6B, if a gossamer structure 300 including the convexfront surface 313 is constituted, a structure such as a huge dome, tent,or the like can be achieved. Also in this case, the detection sensors 12are dispersedly arranged on the gossamer structure 300, and thus theshape thereof can be easily estimated.

It should be noted that the environment in which the gossamer structures200 and 300 are arranged, or the like is not limited. For example, eachstructure may be arranged in space. In this case, for example, each ofthe gossamer structures 200 and 300 functions as a plant on an orbit forspace-based solar power or a huge sunlight shield. Further, eachstructure may be arranged on the ground as a huge construction. In anycase, the shape of each structure can be easily estimated by applicationof the present invention.

REFERENCE SIGNS LIST

-   10 sail-   11 sheet-like member-   12 detection sensor-   13 front surface-   14 back surface-   16 reference plane-   20 spacecraft main body-   30 sunlight-   40 thin-film solar cell-   50, 50 a, 50 b temperature sensor-   100 spacecraft-   200, 300 gossamer structure-   β local incident angle-   n local normal vector-   P arrangement position-   S sun vector

1. A shape estimation method, comprising: setting a reference plane of asheet-like structure on which light is incident; acquiring firstinformation regarding an incident direction of the light with respect tothe reference plane; acquiring second information regarding incidentangles of the light with respect to the sheet-like structure at aplurality of detection positions in two or more states in which theincident directions are different from one another, the plurality ofdetection positions being dispersedly arranged on the sheet-likestructure; and estimating a shape of the sheet-like structure on a basisof the first information and the second information in the two or morestates.
 2. The shape estimation method according to claim 1, wherein aposition in an orthogonal direction orthogonal to the reference plane isestimated for each of the plurality of detection positions of thesheet-like structure, to estimate the shape of the sheet-like structure.3. The shape estimation method according to claim 1, wherein the shapeof the sheet-like structure is monitored.